Question: Given $ m \angle CBD = 6x + 49$, and $ m \angle ABC = 2x + 11$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 11} + {6x + 49} = {180}$ Combine like terms: $ 8x + 60 = 180$ Subtract $60$ from both sides: $ 8x = 120$ Divide both sides by $8$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 2({15}) + 11$ Simplify: $ {m\angle ABC = 30 + 11}$ So ${m\angle ABC = 41}$.